Complex mission optimization for Multiple-UAVs using Linear Temporal Logic

The goal of this paper is to develop models and methods that use complementary strengths of Mixed Integer Linear Programming (MILP) and Constraint Programming (CP) techniques to solve problems that are otherwise intractable if solved using either of the two methods. The class of problems considered in this paper have the characteristic that only a subset of the binary variables have non-zero objective function coefficients if modeled as an MILP. This class of problems is formulated as a hybrid MILP/CP model that involves some of the MILP constraints, a reduced set of the CP constraints, and equivalence relations between the MILP and the CP variables. An MILP/CP based decomposition method and an LP/CP-based branch-and-bound algorithm are proposed to solve these hybrid models. Both these algorithms rely on the same relaxed MILP and feasibility CP problems. An application example is considered in which the least-cost schedule has to be derived for processing a set of orders with release and due dates using a set of dissimilar parallel machines. It is shown that this problem can be modeled as an MILP, a CP, a combined MILP-CP OPL model (Van Hentenryck 1999), and a hybrid MILP/CP model. The computational performance of these models for several sets shows that the hybrid MILP/CP model can achieve two to three orders of magnitude reduction in CPU time.

This study proposes a new mission planning method to perform routing with multiple quadrotors. Unlike conventional routing missions, this study considers the specialized routing mission for quadrotors where there is a visit priority between nodes, and there is a task to be performed at the node. One of our contributions is that a multi-layered hierarchical architecture is designed for mission planning itself at the top level, and for interworking with path planning and flight control required at the lower levels. In mission planning, to determine the optimal pair between agents and visiting nodes and the optimal order of nodes, the optimization problem is designed and solved based on mixed-integer linear programming. Furthermore, we evaluate our method by performing MATLAB and Gazebo co-simulation in a ROS environment.

In this paper, we consider detectability analysis for faults in systems governed by switched affine dynamics. By a fault, we mean a sudden and permanent change in the system dynamics. Given the model of the healthy system, such a fault can be detected via model invalidation, i.e., by collecting past observations over a finite horizon and checking whether these observations can be generated by the healthy system model. Whenever the faulty system model is also available, it is possible to find T, the minimum length of the horizon, with which the fault is guaranteed to be detected eventually (with a T-step delay at most). The procedure for finding such T is known as the fault detectability analysis, and can be accomplished by solving a mixed integer linear program (MILP) for switched affine systems. The main contribution of this work is to show the possibility of reducing the value of T, by augmenting the fault detectability analysis with additional linear temporal logic (LTL) constraints on the switching signals, if any. We express the LTL constraints (restricted in a finite horizon) with a nondeterministic finite state machine called a monitor, which is then transformed into a set of mixed integer linear constraints that can be easily integrated in the MILP used for the detectability analysis. The effectiveness of the proposed approach is illustrated with a drone altitude consensus protocol with switching communication topology.

Anticipated advances in the use and capability of unmanned systems may increase the complexity in mission planning and human-machine teaming, creating challenges for mission performance, safety, and predictability. Verification and validation tools, such as model checking, have been applied to mission planning and is a promising approach but require expertise to use. This article describes the study of one such tool, with an interface that provides the human operator away to communicate their high-level mission goals and objectives to the model checking software without having to learn temporal logics or syntax. We describe the development and refinement of a prototype, as well as an experiment testing if a verification and validation tool can improve mission planning compared to a baseline without a verification and validation tool. Results showed that a tool increased mission planning accuracy, while also increasing mission planning time. Also, subjective workload was not different between the two configurations (tool & baseline). These results indicated that verification and validation tools with a suitable interface can enable humans to communicate mission objectives and constraints to machines, improving performance, safety, and predictability. Results also suggested that additional research to improve this communication would further increase the benefits and impact of these kinds of tools.

In this paper, a scheduling algorithm for multi-processor real-time systems with relative timing constraints and resource constraints is proposed. The proposed algorithm has the capability to satisfy any timing constraints expressed as inequalities in two variables and a constant. This implies that scheduling problems imposed on various timing constraints such as end-to-end timing constraints and/or relative timing constraints, which are known to be difficult to handle, can be solved. Since the problem addressed in this paper is a generalization of some NP-complete problems, it is difficult to solve efficiently. Thus, the goal of the authors is to derive a heuristic algorithm which performs well on many instances of the problem, although in some cases it will take enormous space and time. Experimental results show that the proposed algorithm achieves a success rate of 80% in 3 minutes of computation time.

Joint mission and route planning of unmanned air vehicles via a learning-based heuristic

Restricted Simplicial Decomposition with Side Constraints is a price decomposition method designed for large‐scale nonlinear problems with a set of linear constraints with special structure and an additional set of linear side constraints. The resultant algorithm iterates by solving a linear subproblem subject to the set of structured constraints and a small nonlinear master problem whose feasible region is defined by the intersection of a simplex and the set of side constraints. The number of variables of the master problem is controlled by a parameter named r. The conditions required for the parameter r and the rules for dropping extreme points of the simplex are established for global convergence of the algorithm. Computational results are presented for nonlinear network problems with side constraints.

Allocation problem has always been one of the fundamental issues of building the applications in real-time computing systems. For real-time applications, the allocation problem should directly address the issues of task and communication scheduling. In this context, the allocation of tasks has to fully utilize the available processors and the scheduling of tasks has to meet the specified timing constraints. Clearly, the execution of tasks under the allocation and schedule has to satisfy the precedence, resources, and other synchronization constraints among them. Recently, the timing requirements of the real-time systems emerge that the relative timing constraints are imposed on the consecutive executions of each task and the inter-task temporal relationships are specified across task periods. In this paper we consider the allocation and scheduling problem of the periodic tasks with such timing requirements. Given a set of periodic tasks, we consider the least common multiple (LCM) of the task periods. Each task is extended to several instances within the LCM. The scheduling window for each task instance is derived to satisfy the timing constraints. We develop a simulated annealing algorithm as the overall control algorithm. An example problem of the sanitized version of the Boeing 777 Aircraft Information Management System is solved by the algorithm. Experimental results show that the algorithm solves the problem in a reasonable time complexity.

Traditional scheduling models assume that the execution time of a job in a periodic job-set is constant in every instance of its execution. This assumption does not hold in real-time systems wherein job execution time is known to vary. A second feature of traditional models is their lack of expressiveness, in that constraints more complex than precedence constraints (for instance, relative timing constraints) cannot be modeled. Thirdly, the schedulability of a real-time system depends upon the degree of clairvoyance afforded to the dispatcher. In this paper, we shall discuss Totally Clairvoyant Scheduling, as modeled within the E-T-C scheduling framework [Sub05]. We show that this instantiation of the scheduling framework captures the central issues in a real-time flow-shop scheduling problem and devise a polynomial time sequential algorithm for the same. The design of the polynomial time algorithm involves the development of a new technique, which we term Mutable Dynamic Programming. We expect that this technique will find applications in other areas of system design, such as Validation and Software Verification.

Knowledge representation of mathematical optimization problems and constructs for modeling

In this paper, a finite branch-and-bound algorithm is developed for the minimization of a concave power law over a polytope. Linear terms are also included in the objective function. Using the first order necessary conditions of optimality, the optimization problem is transformed into an equivalent problem consisting of a linear objective function, a set of linear constraints, a set of convex constraints, and a set of bilinear complementary constraints. The transformed problem is then solved using a finite branch-and-bound algorithm that solves two convex problems at each of its nodes. The method is illustrated by means of an example from the literature.

In order to keep a safe access to space in the coming years, it will be necessary to clean the near Earth region from the most dangerous debris like spent satellites or launchers stages. An average removal rate of 5 debris per year is recommended to at least stabilize the current debris population. Successive missions must be planned over the years using similar vehicles in order to limit the development cost. This paper addresses the problem of the mission plan so that they can be achieved at minimal cost by a generic vehicle designed for such Space Debris Collecting missions. The problem mixes combinatorial optimization to select and order the debris among a list of candidates, and continuous optimization to fix the rendezvous dates and to define the minimum fuel orbital maneuvers. The solution method proposed consists in three stages. Firstly the orbital transfer problem is simplified by considering a generic transfer strategy suited either to a high thrust or a low thrust vehicle. A response surface model is built by solving the reduced problem for all pairs of debris and for discretized dates, and storing the results in cost matrices. Secondly a simulated annealing algorithm is applied to find the optimal mission plan. The cost function is assessed by interpolation on the response surface based on the cost matrices. This allows the convergence of the simulated algorithm in a limited computation time, yielding an optimal mission plan. Thirdly the successive missions are re-optimized in terms of transfer maneuvers and dates without changing the debris order. These continuous control problems yield a refined solution with the performance requirement for designing the future Space Debris Collecting vehicle. The method is applicable for a large list of debris and for various assumptions regarding the cleaning program (number of missions, number of debris per mission, total duration, deorbitation scenario, high or low thrust vehicle). It is exemplified on an application case with 3 missions to plan, each mission visiting 5 sun-synchronous debris to be selected in a list of 21 candidates.

In this study, single- and multiobjective optimization approaches for the aircraft arrival sequencing and scheduling problem are proposed. In the single-objective optimization, the constrained position shifting framework is included in the aircraft arrival sequencing and scheduling problem to limit the sequence deviation from the first-come first-served order. A new mixed-integer linear programming formulation is presented by transforming the constrained position shifting framework into a set of linear constraints. In the multiobjective optimization, the number of sequence changes is proposed as a new measure to quantify the sequence deviation from the first-come first-served order. The optimization problem is then solved by using the -constraint method where two objective functions, the total flight time and the number of sequence change, are simultaneously optimized. The performance of the proposed single- and multiobjective optimization algorithms are verified through numerical simulations.

Distribution systems (DS) are a focal connection point for existing and new renewable energy sources. DS have increasing sizes; they connect increasing numbers of renewable energy sources and have a mandate to operate as financial entities seeking to maximize their profits in an electricity market. To achieve these goals, DS require highly efficient planning tools. In this paper, we propose a successive fuzzy mixed integer linear programming (MILP) method for optimally placing and sizing capacitors in a DS that explicitly models induction run wind electric generators (WEGs). The optimization problem is linearized, transformed into a fuzzy MILP model and is solved successively while updating the solution vector. The fuzzy MILP method employs fuzzy models of voltage constraints that are often violated in a planned system that lacks reactive power support. The use of fuzzy constraints makes the proposed solution method very robust by avoiding infeasibility and reducing the need for user expertise. Further, the fuzzy MILP method represents the dual objectives of capacitor cost and annual energy loss minimization as fuzzy sets with individual satisfaction functions. The method maximizes the minimum of these satisfaction functions during optimization. Tests on 69-bus and 2002-bus DS show that the method performs well and is robust.

Volt-VAR control (VVC) in distribution networks is typically performed by autonomously operating voltage regulation devices. In modern distribution systems, most of the control and coordination functions are being carried out by Distribution Management System (DMS), which is a highly digitalized and automated platform. Even though the grid equipment and infrastructure are being modernized, there still exist legacy devices that operate based on local control rules. Integration of such legacy device models into the modern DMS is essential to ensure effective VVC. Hence, this paper proposes optimal coordination of onload tap changers by solving a mixed integer linear programming (MILP)-based mathematical program such that the tap switching operations can be reduced. Unlike existing works, which often ignore the local controller mechanism of LTCs, this work models and integrates the local control rule of the bang-bang controllers of LTCs in the optimal coordination procedure. To this end, the operational principle of the controller is interpreted as a set of mixed-integer linear constraints, enabling the formation of an efficient optimal power flow (OPF) formulation based on a linearized power flow model. Extensive numerical tests on the proposed formulation suggest satisfactory and promising performance.